express y in terms of x

Question

a curve has its derivative dy/dx= 2-12x given that the point (1,3) lies on the curve, express y in terms of x

Answer 1

dy/dx = 2 - 12x

 

dy = (2-12x) dx

y = ∫(2-12x) dx

y = 2x - 6x² + c

 

To find c, plug in the known point (1,3):

 

3 = 2(1) - 6(1²) + c

3 = 2 - 6 + c

3 = -4 + c

7 = c

 

y = -6x² + 2x + 7